How can I grey out only a portion of a photo?

You can place rectangle on image . color it gray and from Blend mode use Color mode.

then you can open Edit->Edit Color->Saturate and change saturation according to your task

Insted rectangle you can use any shape...text..etc

Celine,

With the colour photo on top of the background object, you may:

1) Select the background object and Ctrl/Cmd+X+F+F to have both on top of the photo, then select the bottom one (maybe through the Layers palette) and change the colour to white;

2) Select the colour photo and Ctrl/Cmd+C+F to have the copy at the very top and the original photo at the very bottom;

3) Select the top colour pphoto and the top background object and in the Transparency palette (flyout) tick (Make) Opacity Mask with Clip unticked and Inverse Mask ticked.

That will mask the underlying grey object, and the white object will block the bottom colour photo from showing through the transparency of the mask.